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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 119v, page id 00068198:0238
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(summari
Quaeritur ergo du
n. atdu
sit
nn
= 
utan O= du
n. n+dn
Fn. ntdu Ergo du C= an - du
(du (du
n. nt an utan
nida
no = du
+du
Ergo fiet
Ergo ex 28. per 33,
n. ntdu
n+ u)
le + du l2
Hinc si an = 1  tolletur summa quadratarum fractonum naatium, et
habebitur sum Sn. atdu
sed si e dn sit alius amnerus
constans sma snn et sdu ex se invicem pendebunt.
n. ntdn C
jam  an
t ogt( . ati du = +  est ergo summabilis, t et dabtatio
 sun an sas
et, tt L, 1o est (5i  soli pares vel socsimpans
HHinc sequitur summam quodratorum i a sinctionibus artthmelici de–
nominatoris invenili posse; modo sumg differentia
non sit unitas Ergo si diff. sit unitas haberi prt
tam prope quam quis volet, ob discrimen a summabili
quantum libet, exiguum. Eadem methaus piraliis potentiis.
u 
sent 
praeter
2 =  = + L. Hinc si dn =2 erit hoc
=nn =1
generalius
n+ 1
n- 1
summabile m-1
tit  +  si dn = 2h
nn- ph
n+h n-h
Eit summabilis
M1
Ln-hh
praeter hanc Methodum alia est a quachaturis, vig.
sit (
n posita, du constante sit L =  x + HX + X et
n+ h
sumu est et
2et1
So = . X +  Xet 1+ L X 4L
2C+1
3e+1
um mnt mntmta tantu ergo si X est 1.  summa prodit data progressionis Harmonics
amni muntmude mandu  quae procude semper reducibilis ad quadr. Circ. et Hyp. vel psi
omnes, autem series numervi ravatim qui ubi non est inde-
terminata in exponente possent reduci ad harmoni castux
et potentias et erae vnsu ad hamontems. Nontum oes potentiae n
humionilas reducunt. Itaq circa potentiam sumericarm summas adhuc
haereo Sh+sgi= su sit F  et 9- L 5
map = Smndp + smpdu + Sapdm Cr si M = 1 p = L dm - - dn, = c
in L = ( -2fdn + ( du +s 2 du + du (an. X
mup= Ann n spn. ntdn sim
du habetur =O
n.ntdu
sdn
Ru. ntan
= d fdn
t ntdu
ntan
n. n+ an
fn, ut du
+dn? san
habentur
un, nedu
quia liceb habere suum.  e pab = n b et hac in bris infialita, per quadraturas
summabitir si sit series
nn- bb
nubo infinita habebitium per quadraturas. Ergo et quantulacunque sit b.
an ergo et si sit b=0 videndum foret hic utilis methodus
illa contianitatis.
pro  (an hoc incuil: sit LX + + X +  X  X ere = sydus fiet ydy = + + LX F L X + + X etc
Sinn et X ydy = X + h XX +  X + L Xt etc. = sdx =d 0g 1: -X. Et fiet
yy = (2x logsi  s lgh i + sx logk = log X, log ix
jam alibi desi
Eadem pethodo
oene graditras
 quodem
elum sublatis summutionitus ducetur ad Xy ady + Xdydys, + y dydx = ax :, 1 - X, ubi o sint progross
hadem veltutus et pro i. 8 g. cq erc s po labis
du pabystantes fiet: 291C posita ex constante
ta
mus ingan
am pam tu
+dman p